Remove extra geometry from objects
Manual with good topology

To get the topology in your second image. Select the loops you want to delete with Alt RMB , or in Wireframe mode use border select (B). Then press Delete and choose Edge Loops.  

Manual with N-gons

To delete all edges and vertices on a face and just be left with a large N-gon. Select all the faces on a plane (example everything on the top); then press Delete and choose Limited Dissolve.

Modifiers

If you are less picky about topology, and want a more automatic solution Then use a Decimate modifier. For examples like your's set the Decimate modifier to Planar, then adjust the angle limit to suit your needs.